middle school vs secondary school

middle school and secondary school both are nouns.

Word	Noun	Adjective	Verb	Adverb
middle school	Yes	No	No	No
secondary school	Yes	No	No	No

As nouns, middle school and secondary school are synonyms defined as:

middle school and secondary school: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other synonyms of middle school include Gymnasium, lycee, lyceum.

middle school (noun)	secondary school (noun)
a school for students intermediate between elementary school and college; usually grades 9 to 12	a school for students intermediate between elementary school and college; usually grades 9 to 12